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I s there Enough Evidence to Verify a Claim?

I s there Enough Evidence to Verify a Claim?.

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I s there Enough Evidence to Verify a Claim?

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  1. Is there Enough Evidence to Verify a Claim? According to an article from MSN, the Minnesota Timberwolves current roster consists of 9 Caucasian players, and 6 African American players. In the NBA, 3 out of 4 players are African American. Is this enough evidence to state that the Minnesota Timberwolves are discriminating? In January of this year, there was a lot of upheaval about the cabinet that President Obama elected-all white men. Does this mean that Pres. Obama is somehow discriminating against women or those of another ethnicity? A food distributer claims that their hot dogs are made with 80% organically raised beef. You take a sample of 25 of their hot dogs and find that only 67% of the meat products were made with organic beef. Does this mean that the distributer is trying to sell products that contain less then advertised?

  2. Hypothesis Testing (day 1) Writing Null and Alternative Hypothesis

  3. What’s the Probability? Looking at our earlier claims, it’s not enough to just say that something looks suspicious. We need to provide mathematical proof! To do so, we use the laws of probability and the Properties of Normal Distributions…

  4. Ex 1: A car company advertises that their trucks can tow an average 3,500 lbs. Miss K wants to test their claim. In order to perform a test, we need to have hypothesis’ to state what we believe will happen. Write a Null Hypothesis and an Alternative Hypothesis for the situation.

  5. Ex 1: A car company advertises that their trucks can tow an average 3,500 lbs. Miss K wants to test their claim. Write a Null Hypothesis and an Alternative Hypothesis for the situation. Note: We always write our hypothesis’ in terms of the population parameters.

  6. Ex 2: You are playing a game with your friend where you have to roll 1 die. You begin to suspect that your friend may be cheating. One number seems to be coming up more then the others. Write a Null and Alternative Hypothesis to test the proportion of times that number appears. The distribution of rolls for 1 die should be as follows:

  7. Formats for Null and Alt. Hypothesis’ For Proportions: For Means:

  8. Warm Up: To find the standard score for means: How do you think we could find the standard score for proportions? Note: The standard deviation uses the population proportion (p).

  9. Why Use so many p’s? p : Population Proportion p-value : probability

  10. Hypothesis Testing (day 2) Significance Tests

  11. Ex 1: You are playing a game with your friend where you have to roll 1 die. You begin to suspect that your friend may be cheating. You observe that a 5 comes up 6 times out of the 10 rolls she made. Using this evidence does it appear the she is cheating? The distribution of rolls for 1 die should be as follows: Step 1: Write a Null Hypothesis and an Alternative Hypothesis.

  12. Ex 1: You are playing a game with your friend where you have to roll 1 die. You begin to suspect that your friend may be cheating. You observe that a 5 comes up 6 times out of the 10 rolls she made. Using this evidence does it appear the she is cheating? This means you will use p = .17 when finding the z-score.

  13. Ex 1: You are playing a game with your friend where you have to roll 1 die. You begin to suspect that your friend may be cheating. You observe that a 5 comes up 6 times out of the 10 rolls she made. Using this evidence does it appear the she is cheating? Step 3: Find the p-value (probability). P(< 3.61) = normalcdf(-E99, 3.61) = .9998 Thus the probability above 3.61 is: 1-.9998 = .0002 Use: normalcdf(-E99,z-score) or Z-Table p-value = .0002

  14. Ex 1: You are playing a game with your friend where you have to roll 1 die. You begin to suspect that your friend may be cheating. You observe that a 5 comes up 6 times out of the 10 rolls she made. Using this evidence does it appear the she is cheating? p-value = .0002 So… now what? Step 4: Interpret what you found. With this probability, you have just found how likely it is for a normal die to roll six 5’s out of 10 rolls. This is very unlikely with just pure luck (although it still could happen)! In order to state some sort of concrete conclusion, we need to establish a point at which the event is so unlikely-it’s nearly impossible. To be continued…

  15. Ex 2: In a recent year, 73% of first-year college students responding to a national survey identified “being very well- off financially” as an important personal goal. A state university finds that an SRS of 132 of 200 of its first-year students say this goal is important. Does this suggest that less students then expected share this belief? Step 1: Write a Null Hypothesis and an Alternative Hypothesis.

  16. Ex 2: In a recent year, 73% of first-year college students responding to a national survey identified “being very well- off financially” as an important personal goal. A state university finds that an SRS of 132 of 200 of its first-year students say this goal is important. Does this suggest that less students then expected share this belief? Step 3: Find the p-value (probability). normalcdf(-E99,-2.33) The probability below a z-score of -2.33 is .0099 . p-value = .01 Step 4: Interpret what you found. This seems very unlikely to occur just by chance, we will examine it in more detail later…

  17. Exit Slip: A news article claimed that 5% of all high school athletes used some form of steroids when training. You take a sample of 1079 high school students and find that 52 of them have a form of detectible steroids in their system. Has steroid use gone down? Perform a hypothesis test to verify your conclusion.

  18. If I were to tell you… The probability of an event occurring is .04, how likely is it that that event will happen? *Keep in mind that we are looking at the probability of different events happening. And we want to use those probabilities to test hypothesis.’

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